Question

True or False If the average rate of change of a linear function is $\frac{2}{3}$, then if $y$increases by $3$,$x$will increase by$2$.

Short answer

The given statement is false.

Step-by-step solution

Given information

If the average rate of change of a linear function is$\frac{2}{3}$ , then if $y$increases by$3$ , $x$will increase by$2$ .

Solution

Linear functions have a constant average rate of change. That is, the average rate of change of a linear function $y=mx+b$is

$\frac{∆y}{∆x}=m.$

Here, $∆x=2$and $∆y=3,$then $m=\frac{∆y}{∆x}=\frac{3}{2}.$

Final answer

Hence, the given statement is false.